You need a 30-year, fixed-rate mortgage to buy a new home for $235,000. Your mortgage bank will lend you the money at an APR of 5.35 percent for this 360-month loan. However, you can afford monthly payments of only $925, so you offer to pay off any remaining loan balance at the end of the loan in the form of a single balloon payment. How large will this balloon payment have to be for you to keep your monthly payments at $925?

To find out the size of the balloon payment needed to keep monthly payments at $925, we need to calculate the remaining loan balance at the end of the loan term.

First, we convert the APR to a monthly interest rate by dividing it by 12 and converting it to a decimal form. The monthly interest rate in this case would be 5.35% / 12 = 0.0044583.

Next, we calculate the monthly payment amount using the formula for a fixed-rate mortgage:

P = (A * r) / (1 - (1 + r)^(-n))

Where:
P = monthly payment
A = loan amount ($235,000)
r = monthly interest rate (0.0044583)
n = number of payments (360 months)

Substituting the values into the equation:

P = (235,000 * 0.0044583) / (1 - (1 + 0.0044583)^(-360))
P ≈ $1,147.29

We see that the monthly payment amount would be approximately $1,147.29, which is higher than what you can afford.

Now, we need to determine the remaining loan balance after 360 payments of $925.

To calculate the remaining balance, we use the formula for the future value of an ordinary annuity:

FV = P * ((1 + r)^n - 1) / r

Where:
FV = future value of the remaining balance
P = monthly payment ($925)
r = monthly interest rate (0.0044583)
n = number of payments (360 months)

Substituting the values into the equation:

FV = 925 * ((1 + 0.0044583)^360 - 1) / 0.0044583
FV ≈ $57,496.56

Therefore, the balloon payment needed to keep monthly payments at $925 is approximately $57,496.56.

To calculate the balloon payment, we first need to calculate the monthly payment for the mortgage.

The formula to calculate the monthly payment is:

M = P * r * (1 + r)^n / ((1 + r)^n - 1)

Where:
M = Monthly payment
P = Loan amount ($235,000)
r = Monthly interest rate (APR / 12)
n = Number of payments (30 years * 12 months per year)

First, let's convert the APR to a monthly interest rate.

Monthly Interest Rate = APR / 12
= 5.35% / 12
= 0.446%

Now, let's calculate the number of payments.

Number of Payments = Number of Years * 12
= 30 * 12
= 360

Let's plug these values into the formula to calculate the monthly payment:

M = $235,000 * 0.00446 * (1 + 0.00446)^360 / ((1 + 0.00446)^360 - 1)

Calculating this, the monthly payment comes out to be approximately $1,314.19 (rounded to two decimal places).

Since you can afford monthly payments of only $925, there is a shortfall of $389.19 ($1,314.19 - $925).

To calculate the balloon payment, we need to find the remaining loan balance at the end of the term. Here's how:

Remaining Loan Balance = Loan amount * (1 + r)^n - (M * ((1 + r)^n - 1) / r)

Rearranging the formula to solve for the balloon payment:

Balloon Payment = Remaining Loan Balance

Let's plug in the values:

Remaining Loan Balance = $235,000 * (1 + 0.00446)^360 - ($1,314.19 * ((1 + 0.00446)^360 - 1) / 0.00446)

Calculating this, the balloon payment comes out to be approximately $120,835.07 (rounded to two decimal places).

Therefore, the balloon payment will have to be approximately $120,835.07 for you to keep your monthly payments at $925.

I will assume that the rate is 5.35% per annum, compounded monthly, that is

i = .053/12 = .0041666..
let the balloon payment be x
925(1.0041666..^360 - 1)/.0041666... + x = 235,000(1.004166...)^360

solve for x
Tell me what you got.

If you get an answer of over $340,000 , don't be alarmed, it is correct.
This scenario is really unreasonable, the actual payments on this mortgage
should have been over $1300 per month, so this mortgage was beyond your
budget.